Library / /51 of 176

, 1998

Algebra Difficulty 2.0 Junior Prove it Canada

Show that if $x^2+px+q=0$ and $x^2+px-q=0$ both have integer solutions, then it is possible to find integers $a$ and $b$ such that $p^2=a^2+b^2$ (i.e. $(a,b,p)$ is a Pythagorean triple).

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.